How store the sourdough

Hi. Firstly sorry for my english but I'm not American or English and I still learning :)

I have a question how to store the sourdough. I have mature sourdough culture (rye sourdough) and I wanna use it to make bread daily. If I take a little dose of sourdough to make bread, can I just refreshed the rest of my sourdough (add water and flour) and leave it for 12 hours in room temperature? The wild yeast and bacteria after 12 hours will still alive? Or mayby I should put the sourdough to the fridge? But I have read that "(...)in a lower temperature (below 46°F) part of the flora of the culture may be destroyed(...) "